A small circular loop of radius a is placed inside a circular loop of radius b(ba) . The loops are coplanar and concentric. The mutual inductance of the system is proportional to

Question

A small circular loop of radius a is placed inside a circular loop of radius b(b>>a) . The loops are coplanar and concentric. The mutual inductance of the system is proportional to (A) (a2/b) (B) (a/b2) (C) (a/b) (D) a × b

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/048a9895813a73e37057f45774da7fd8-.png" /> Flux through smaller coil =B × π a2 and B at centre of large coil B=(μ0 I/2 b) ∴ φ=((μ0 I/2 b)) × π a2 =((μ0 π/2))[(a2/b)] I φ=M I . ∴ φ propto (a2/b)

Q. A small circular loop of radius $a$ is placed inside a circular loop of radius $b (b >> a) .$ The loops are coplanar and concentric. The mutual inductance of the system is proportional to

$\frac{a ^{2}}{b}$

$\frac{a}{b ^{2}}$

$\frac{a}{b}$

$a \times b$

Flux through smaller coil
$= B \times π a^{2}$
and $B$ at centre of large coil
$B = \frac{μ _{0} I}{2 b}$
$∴ ϕ = (\frac{μ _{0} I}{2 b}) \times π a^{2}$
$= (\frac{μ _{0} π}{2}) [\frac{a ^{2}}{b}] I$
$ϕ = M I .$
$∴ ϕ \propto \frac{a ^{2}}{b}$

Q. A small circular loop of radius a is placed inside a circular loop of radius b(b>>a). The loops are coplanar and concentric. The mutual inductance of the system is proportional to

ba2​

b2a​

ba​

a×b